Our Sun will puff out gas and lose mass in its final stage of life, before becoming a white dwarf. The Earth's orbit will get thrown out of whack, and the same for other planets. Could they even collide? It seems unlikely to me - there's a lot of room in space - but I haven't done any calculations. Boris Gänsicke and colleagues decided to actually look. They checked out 80 white dwarfs and found 4 whose atmospheres contain oxygen, magnesium, iron, silicon, and a small bit of carbon - just the elements expected if the stars are absorbing dust from former planets. "If you could shred the Earth into dust and put it into the white dwarf, it would match the chemical composition."

+Aleks Scholz - your scenario might make more sense. But the National Geographic article I linked to wrote "The changing orbits would sometimes lead to planets crashing into each other, churning up chunks of rocky debris."﻿

Regarding the "lot of room in space" effect, there's also lots of time. Collisions that would be very unlikely over a year or century may be almost certain over a million (Earth) years or a million centuries. Frequent is the new rare.﻿

Thanks, +Aleks Scholz! I was looking for the paper this story was about, but gave up too soon. The main author didn't include it on his webpage. It says

"... the rapidly growing number of white dwarfs [that we've studied] that are accreting from circumstellar discs unambiguously demonstrates that debris from the tidal disruption of main-belt analogue asteroids or minor planets or Kuiper-belt like objects, likely perturbed by unseen planets, is the most likely origin of photospheric metals in many, if not most polluted white dwarfs."

So, the stuff about planets crashing into each other seems to be the journalists' imagination.﻿